Appendix 1
Further details on the demographic projections
5.1 Fertility
The most common fertility indicator is the total fertility rate. An alternative, however, is the number of children successive cohorts of women had borne by the time they reached the end of their childbearing at age 50, which is known as ‘completed fertility’. Completed fertility rates for New Zealand are graphed in Appendix Figure 1. The figure shows, for instance, that women born in 1905 had given birth to an average of 2.5 children by the time they turned 50.
- Appendix Figure 2 - Age-distribution of childbearing, for cohorts of women
- Note: Hatched lines denote ‘partly pre-determined values.’ See text for details.
Appendix Figure 2 shows how successive cohorts distributed their childbearing over their reproductive lives. It shows, for instance, that the cohort born in 1905 had achieved only 30% of their completed fertility by age 25, whereas the cohort born in 1950 had completed 50%.
Demographers have traditionally projected fertility by constructing a future path for the total fertility rate, making an assumption about the age-distribution of fertility, and then deriving the age-specific rates. This approach is simple and transparent. It may not, however, perform well for populations like that of New Zealand where women seem to be systematically shifting childbearing later into their reproductive years. Demographers have traditionally incorporated these effects in an informal way: the UN Population Division, for instance, projects an increase in European fertility rates partly on the grounds that women are delaying childbearing.
Many demographers have become dissatisfied with the informal approach. Some have attempted to develop systematic procedures for stripping out the ‘tempo’ effects (Bongaarts and Feeney 1998), but these are still controversial, and require data not available for New Zealand. In this paper, a simple type of the ‘cohort completion’ (Morgan and Chen 1992) approach was used.
The first step was to construct paths for completed fertility, shown in Appendix Figure 1. Two series were constructed. In the ‘base’ series, completed fertility was assumed to decline linearly from 2.5 for the cohort born in 1950 to 1.9 for the cohort born in 2000, and to remain constant for subsequent cohorts. In the ‘alternative’ variant, completed fertility was assumed to decline to 1.2 for the cohort born in 1995.
The second step was to choose values for the age-pattern of fertility, shown in Appendix Figure 2. Cohorts born between 1950 and 1980 had had at least some of their children by 2000. This means that, once values for completed fertility had been chosen, some or all of the age-pattern was already determined. These partially pre-determined values are shown as hatched lines in Appendix Figure 2. Trends in age patterns were extended beyond the hatched lines by choosing a pattern for the 2025 and linearly interpolating. The pattern chosen for the 2025 cohort was similar to that of the early 20th Century cohorts, though with somewhat higher fertility in the 40s, on the assumption that medical progress will make delayed childbearing increasingly feasible.
Once completed fertility and its age-pattern had been chosen, rates for age-specific fertility and the total fertility rate could be read off. The results for the total fertility were shown in Figure 1 in the main text. In the base series, total fertility rate actually rises somewhat over the period 2000-2010. This is a result of the assumption, depicted in Appendix Figure 2, that the backward shifting of fertility will start to taper off by this time.
5.2 Mortality
The main text discussed the projection of life expectancies, but not age-specific mortality rates. The relationship between life expectancies and age-specific mortality rates is complex, and there are variety of methods for deriving age-specific rates consistent with a given level of life expectancy and with a population’s historical age-pattern of mortality. Statistics New Zealand scales all single-year mortality rates by a single percentage until the desired life expectancy is reached. We used a ‘logit life table system’ (Preston et al 2001: 119-201), with the 1998-2000 New Zealand life table as the standard, and the governing the relationship between child mortality and adult mortality held constant. Because the alternative scenario had life expectancies rising to very high levels by the end of the projection period, it was necessary to extend the standard life table into higher age-groups. This was done using the 'Kannisto model' as described in Thatcher, Kannisto, and Vaupel (1998).
